We did our kitchen last year. I went with a dark blue countertop (engineered stone) and 4" ceramic tiles for a backsplash like you want.

We chose tiles for the back splash that matched the larger tiles for the kitchen floor. Where you have hardwood floors, that's not possible. I'd go with a color that complements the countertop but is much lighter. I recommend you have the contractor use a grout sealer on the tile grout to prevent stains from getting a foothold in the porous grout.

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"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan

Since your kitchen is so warm looking already you probably want to keep that trend going. How high do you need your backsplash? If you want to cover the whole bit I'd go with a natural slate or marble to complement the counter. You can do some decorative stuff just with moving tiles around. My backsplash is rather small. I only have one row of 6 inch tiles with a one inch border on top. Suits me. I think theres a picture of it on the site somewhere.

__________________You're only given a little spark of madness. You mustn't lose it. Robin Williams Alix

I think a tile with little sheen would be nice and I definitely think a complimentary color would be important - I suggest greens. A lot depends on other areas / themes in your house.I think you've max'd out on the warm, rich browns with the flooring and cabinets.